Categorical data Professor Jarad Niemi STAT 226 - Iowa State - PowerPoint PPT Presentation

Categorical data Professor Jarad Niemi STAT 226 - Iowa State University August 28, 2018 Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 1 / 19

Outline Distribution, frequency table Bar chart Pareto chart Pie chart Mode and median Contingency table Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 2 / 19

Categorical data Distribution and frequency tables Definition The distribution of a variable is the collection of possible values the variable can take and how often each value occurs. Definition A frequency table is a summary that shows the distribution of a variable. For categorical variables, we can use the following to understand the distribution of a variable: frequency table, bar chart, Pareto chart, pie chart, mode, median, and contingency table. Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 3 / 19

Categorical data Majors Major College Clsfn.Year 1 P BUS M 3 2 P BUS M 3 3 AG B A 2 4 MKT M 2 5 ACCT M 2 6 P BUS M 2 7 ACCT M 2 8 AG B A 3 9 BUS U M 2 10 P BUS M 2 Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 4 / 19

Categorical data Majors summary Major College Clsfn.Year P BUS :65 A:25 Min. :1.000 AG B :24 H: 1 1st Qu.:2.000 ACCT : 3 M:74 Median :2.000 MKT : 3 S: 1 Mean :2.485 BUS U : 2 3rd Qu.:3.000 A M D : 1 Max. :4.000 (Other): 3 Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 5 / 19

Categorical data Recode Year Major College Clsfn.Year Year P BUS :65 A:25 Min. :1.000 Freshman : 2 AG B :24 H: 1 1st Qu.:2.000 Sophomore:54 ACCT : 3 M:74 Median :2.000 Junior :39 MKT : 3 S: 1 Mean :2.485 Senior : 6 BUS U : 2 3rd Qu.:3.000 A M D : 1 Max. :4.000 (Other): 3 Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 6 / 19

Categorical data Frequency table Frequency table Majors: A M D ACCT AG B AN S BUS U ECON FIN MKT P BUS 1 3 24 1 2 1 1 3 65 College: A H M S 25 1 74 1 Year: Freshman Sophomore Junior Senior 2 54 39 6 Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 7 / 19

Categorical data Bar chart 40 count 20 0 Freshman Sophomore Junior Senior Year Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 8 / 19

Categorical data Bar chart 40 Year Freshman count Sophomore Junior Senior 20 0 Freshman Sophomore Junior Senior Year Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 9 / 19

Categorical data Bar chart Senior Junior Year Sophomore Freshman 0 20 40 count Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 10 / 19

Categorical data Bar chart 0.4 prop 0.2 0.0 Freshman Sophomore Junior Senior Year Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 11 / 19

Categorical data Bar chart 60 40 count 20 0 A M D ACCT AG B AN S BUS U ECON FIN MKT P BUS Major Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 12 / 19

Categorical data Pareto chart 60 40 count 20 0 P BUS AG B ACCT MKT BUS U A M D AN S ECON FIN Major Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 13 / 19

Categorical data Pie chart 0/100 Major 1 P BUS AG B ACCT factor(1) MKT 75 25 BUS U A M D AN S ECON FIN 50 Percentage Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 14 / 19

Categorical data Pie chart Arguments against pie charts https://www.darkhorseanalytics.com/blog/salvaging-the-pie Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 15 / 19

Categorical data Pie chart Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 16 / 19

Categorical data Mode Mode Definition The mode is the most common value. The mode may not be unique. P BUS AG B ACCT MKT BUS U A M D AN S ECON FIN 65 24 3 3 2 1 1 1 1 A H M S 25 1 74 1 Freshman Sophomore Junior Senior 2 54 39 6 Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 17 / 19

Categorical data Median Median Definition The median of an ordinal variable is the middle value when the values are ordered. [1] Freshman Freshman Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore [12] Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sopho [23] Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sopho [34] Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sopho [45] Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sophomore Sopho [56] Sophomore Junior Junior Junior Junior Junior Junior Junior Junior Junior Junior [67] Junior Junior Junior Junior Junior Junior Junior Junior Junior Junior Junio [78] Junior Junior Junior Junior Junior Junior Junior Junior Junior Junior Junio [89] Junior Junior Junior Junior Junior Junior Junior Senior Senior Senior Senio [100] Senior Senior Levels: Freshman Sophomore Junior Senior Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 18 / 19

Categorical data Contingency table Contingency table Definition A contingency table shows the distribution of one variable in the rows and another in the columns. Year Major Freshman Sophomore Junior Senior P BUS 2 33 27 3 AG B 0 12 10 2 ACCT 0 2 1 0 MKT 0 3 0 0 BUS U 0 2 0 0 A M D 0 1 0 0 AN S 0 0 1 0 ECON 0 0 0 1 FIN 0 1 0 0 Professor Jarad Niemi (STAT226@ISU) Categorical data August 28, 2018 19 / 19